Question

What is the slope and intercept for $y=\dfrac{1}{5}x$ and how would you graph it?

Answer 1

Hint: In this question, we are given an equation of line and we need to find the slope and intercept of the line. After that we need to draw a graph for that line. For calculating the slope and the intercept we will convert the equation in the slope intercept form i.e. y = mx+c where m is the slope and c is the intercept and compare. To draw the graph, we will find some values of x and find the values of y. We will plot these points on the graph and then draw a line passing through them which will be the required line.

Complete step-by-step answer:
Here we are given the equation of line as $y=\dfrac{1}{5}x$. We need to find the slope and intercept of this line. We also need to draw a graph for this line.
Let us first find the slope and intercept of this line.
As we know that, slope intercept form of an equation of line is of the form y = mx+b where m is the slope and b is the intercept. So let us compare the given line with this form to get the slope and intercept.
We are given the equation as $y=\dfrac{1}{5}x$. Comparing y = mx+c we see that $m=\dfrac{1}{5}$ and c = 0. Hence the slope of the line is $\dfrac{1}{5}$ and the intercept is 0 which means the line meets the y axis at y = 0. Hence $\text{Slope}=\dfrac{1}{5}$. Intercept = 0.
Now let us try to plot a graph for this line. For this let us find some coordinates of the point on the line. Let us substitute some values of x to get values of y. For ease, let us select values of x as multiple of 5 to get the values of y as integers only.
Taking x = 5 we get $y=\dfrac{1}{5}\times 5\Rightarrow y=1$.
Taking x = -5 we get $y=\dfrac{1}{5}\times \left( -5 \right)\Rightarrow y=-1$.
Taking x = 0 we get $y=\dfrac{1}{5}\times 0\Rightarrow y=0$.
Hence we have obtained 3 points that will lie on the line $y=\dfrac{1}{5}x$. The coordinate of the points are (5,1), (-5,-1), (0,0). So let us plot these points and then draw a line passing through them. This will be our required line. The graph looks like this,

Note: Students should not get confused between m and c as the slope and the intercept. Note that, we generally require only two points to draw a line on the graph. Take care of the signs of coordinate while plotting them on the graph.